IDEAS home Printed from https://ideas.repec.org/a/hin/jnlaaa/8495254.html

A Generalized Topology Approach to Trajectory Convergence in Nonautonomous Evolution Equations With Monotone Operators

Author

Listed:
  • Boushra Abbas

Abstract

This paper investigates the application of β-open sets to the convergence analysis of nonautonomous evolution equations governed by maximal monotone operators in Hilbert spaces. β-open sets are a class of generalized open sets introduced by Njåstad (1965), which coincides with the class of semiopen sets by Levine (1963). We first examine whether the properties of β-open sets, which form a generalized topology (not a classical topology), can offer a more flexible framework for studying trajectory convergence. And then we discuss potential advantages in relaxing certain coercivity conditions in contrast with analyses in standard metric or weak topologies, while addressing the non-Hausdorff nature and limited intersection closure of β-open sets. Examples from optimization problems (variational inequalities and sparse regression) and numerical insights from image denoising applications are utilized to illustrate the benefits of the approach. The paper highlights key challenges and outlines directions for further theoretical and computational development.

Suggested Citation

  • Boushra Abbas, 2026. "A Generalized Topology Approach to Trajectory Convergence in Nonautonomous Evolution Equations With Monotone Operators," Abstract and Applied Analysis, Hindawi, vol. 2026, pages 1-7, March.
    • Handle: RePEc:hin:jnlaaa:8495254
    DOI: 10.1155/aaa/8495254
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/aaa/2026/8495254.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/aaa/2026/8495254.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/aaa/8495254?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hin:jnlaaa:8495254. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.